Calculation of frost heaving pressure in an open fissure in a freeze-thaw period

Frost heaving pressure (FHP) is crucial for understanding the damage to jointed hard rocks in cold, high-altitude regions. Despite well-developed methodologies for FHP during the freezing process, studies exploring the impact of a freeze-thaw period remain scarce. This study categorized the FHP in open-jointed hard rock into six stages, including oscillating increase during the sealing of fissures by ice wedges, sharp rise accompanied by ice wedge slipping, sharp decrease from crack propagation, gradual decrease resulting from the progressive attenuation of cohesive stress, second increase due to ice segregation, and second decrease caused by the ice-water phase transition. A model for FHP in an open-fissured rock during a freeze-thaw period was established, accounting for interactions among ice, water, and rock. A freeze-thaw test was conducted on a rock block to validate the model. The results indicated that the decline in FHP after the first peak is attributed to crack propagation and the progressive attenuation of cohesive stress. The decline can be calculated by updating the fissure length, considering the fracture process zone, and employing a time-variable Weibull probability model. In low-permeability rock, the early melting-induced FHP increase results from melting water migrating into deeper fissures, with the peak lower than the first FHP peak. The decline in FHP during the mid-to-late melting stage can be characterized by the reverse process of water-ice phase transition. The study replicates the FHP in a freeze-thaw period, providing a theoretical foundation for identifying damage in jointed hard rocks.